MTH 173 & MTH 174, Calculus Fall 2012, King William High School Dual Enrollment Laura Vecchione, Mathematics Instructor Course Syllabus

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MTH 173 & MTH 174, Calculus Fall 2012, King William High School Dual Enrollment Laura Vecchione, Mathematics Instructor Course Syllabus Instructor Contact Information Name: Laura Vecchione Email:

1 MTH 173 & MTH 174, Calculus Fall 2012, King William High School Dual Enrollment Laura Vecchione, Mathematics Instructor Course Syllabus Instructor Contact Information Name: Laura Vecchione Phone: Instructor Availability: Please see me for a pass to stay after school or come in before school for extra tutoring available most days upon request. Response Time: I usually respond to s within 2 day, some weekends I may not have internet access. If you have not received a response in 48 hours please send another . Please include the student s name and subject in the . Introduction: Calculus is the branch of mathematics which measures the rate at which quantities change. This course is dual enrollment with Rappahannock Community College (if you have passed their Placement Test), which means that it includes the first two semesters of college level calculus. At the community college, these two semesters are worth 10 credits. For this reason, we will make every attempt to cover the same chapters that they cover. Further colleges do not award credit for a D as high schools do. You cannot receive college credit for MTH 174 unless you have earned a C or better in MTH 173. A full understanding of the subject matter of this course will not occur unless you are prepared to do extensive work on your own, outside of class. You must come to class prepared whether this means reading the text and all of its examples in detail or attempting the solution of all the problems assigned. I cannot answer your questions if you do not do enough work to have questions. Please be sure to ask questions if you do not fully understand something. It is extremely important to keep up in this class as most of the material builds upon itself. We can also make arrangements to meet outside of class if needed. Classroom Procedures: 1. Students are expected to be in their seats when the tardy bell rings and to remain in there until dismissed by the teacher. 2. Students are required to bring all materials to class - textbooks, notebooks, paper and pencils - every day. 3. Work areas and desks are to be kept clean. 4. Snacks and drinks are not permitted in classrooms with the exception of plain water 5. Any electronic devices that are seen or heard will be confiscated unless you have prior permission from the administration or teacher. 6. Make every effort to use the restroom between classes. 7. Make-up work needs to be completed within the same number of days as the number of absences, not to exceed five days, except with administrative permission. It is the student s responsibility to obtain the assignment from the assignment notebook and make arrangements with the teacher to make up graded work. It is wise to make arrangements with another student for class notes. 8. Tardies to class: 1 = warning 2 = phone call home 3 = detention 4 = referral 5 = referral 6 = 1 absence and referral 9. All interim grade reports need to be signed by a parent 10. Computer use policy will be strictly applied. These computers are not to play games or use the internet for entertainment. Calculators are not for game use. 11. Test corrections will be used to increase your 9 weeks grade 12. The Honor code will be strictly enforced. Consulting on classwork/homework is not the same as copying someone s work.

2 Course Description MTH 173: Presents analytic geometry and the calculus of algebraic and transcendental functions including the study of limits, derivatives, differentials, and an introduction to integration along with their applications. Designed for mathematical, physical and engineering science programs. Exam Week MTH 173: January 21 st -24 th, 2013 KWHS exam schedule RCC Withdrawal Date: October 29 th, 2012 Course Credit:. Lecture 5 hours per week. 5 Credits Prerequisites: Prerequisites are MTH "Precalculus with Trigonometry" or MTH "Precalculus II" or (1) satisfactory score on an appropriate proficiency examination and (2) two units of algebra, one of geometry, one-half unit each of trigonometry and precalculus. Course Objectives MTH 173 The students successfully completing MTH 173 should be able to: 1. define a function, the limit of a function at a point, continuity at a point and differentiability at a point, 2. state and show uses of the Mean Value Theorem, 3. computes the derivatives of polynomials, rational functions, and composite algebraic functions, and trigonometric functions, natural logarithmic and exponential functions, 4. differentiate implicitly, 5. apply the techniques of differential calculus to the problem of curve sketching, 6. apply differentiating techniques to find velocity and acceleration and to solve related rate and maximum/minimum problems, 7. defines the anti-derivative of a function and defines the Riemann integral, 8. interpret the relationship between anti-differentiation and differentiation, 9. state and apply the Fundamental Theorem of Calculus, 10. state the important properties of the integral, 11. solve problems involving anti-derivatives and areas, 12. state and use the Mean Value Theorem for Integrals, Course Description MTH 174: Continues the study of analytic geometry and the calculus of algebraic and transcendental functions including rectangular, polar, and parametric graphing, indefinite and definite integrals, methods of integration, and power series along with applications. Exam Week MTH 174: June 9 th - 12 th, 2013 KWHS exam schedule, seniors: June 2 nd 6 th RCC Withdrawal Date: March 24 th, 2013 Course Credit:. Lecture 5 hours per week. 5 Credits Prerequisites: Satisfactory completion of MTH "Calculus with Analytic Geometry I" or equivalent. (C) Course Objectives MTH solve problems involving volume, arc-length work, and centroids of plane areas, 2. differentiates and integrates expressions involving transcendental functions, 3. define conics, vectors, sequence, limit of a sequence, infinite series, convergence 4. and divergence of a series, 5. solve problems involving conics, rotation and translation of coordinate axes 6. and polar coordinates, 7. find areas bounded by curves in polar form, 8. solve problems involving parametric equations, vectors, 9. solve problems involving improper integrals and infinite limits of integration, 10. find series representations of functions and use Taylor's Theorem with Remainder, 11. differentiates and integrates power series, solve problems in indeterminate form, and obtain competency in the use of a graphing utility and CAS in the topics below.

3 Method of Instruction Lecture, discussion, text readings, group activities, and computer programs are all used to cover the material. Important concepts are outlined during class discussions and summarized at the end of each unit. The student should understand and be able to elaborate on these concepts based on lecture, text, and practice done outside of class. Key terms are defined for each chapter the student should be familiar with the spelling, definition, and usage of these terms. The student is expected to attend class and to perform to the best of his/her ability on all activities. Reading the text before class is strongly recommended to prepare the student to participate and maximize his/her learning. Pertinent questions and discussion during lecture are encouraged. The student is expected to keep up with his/her course work, and, if necessary, consult with the instructor as needed as described above. Calculator Use: Students will be expected to demonstrate proficiency in the use of a graphing calculator during this course. Instructional Materials Required Materials - Bound text Thomas Calculus 12 th edition by Thomas. Publisher Pearson ISBN Graphing calculator TI -83 graphing calculators will be available in class and may be checked out from the Ms. Dana Walker - Supplies needed daily for class notebook, looseleaf paper, pencils, textbook - Posterboard and 3-prong folders for projects. Grading and Evaluation Success in this course depends greatly on your participation in class and on projects. Your grade will be based on the following scale: 89.5%-100% A 79.5%-89.4% B 69.5%-79.4% C 59.5%-69.4% D 59.4% and below F The student s grade will be based on homework, classwork, quizzes, tests, and test corrections. Homework will only be assigned as needed. We will cover limits, derivatives, chain rule, 1st and 2nd derivative tests, antiderivatives, definite integrals, and u-substitution during the first semester. During the second semester we will cover solids of revolution, hyperbolic trig, integration by parts and with partial fractions, and trig integrals. Tests will usually occur at the middle and end of each chapter. There will also be a mandatory comprehensive exam each semester as required by the college. You cannot be exempt from either of the exams. All grades will be posted in Powerschool. Tests will count as 40% of the 9 weeks grade; quizzes will count 30%; and homework and classwork together will count 30%. You will be responsible for keeping a notebook containing both your class notes and solved problems. There will probably be one quiz each week. Test corrections will be used as both a teaching tool and a means of improving test scores. Corrected tests will be used as a study guide for each semester exam. Each exam will count 20% each semester. Attendance Policy The college s attendance policy will be enforced, students who have missed more than 20% of the scheduled class meetings at the withdrawal date will be withdrawn from the class unless the student contacts the instructor and asks to remain in the class. Testing Policy A midterm and a final will be given in class. Students who miss the midterm or final without prior approval or proper documentation of absence will receive a zero for that test.

4 Learning Sequence Major Topics To Be Included 1 st Semester MTH 173 A. Optional Review of Pre-Calculus Introductory Topics (not included) 1. Mathematical Induction, 2. Completeness Axiom, 3. Inequalities, 4. Linear Equations 5. Absolute Values, 6. Circles and Parabolas, 7. Functions, a. Definition, b. Domain and Range c. Operations d. Examples and classifications of important functions such as polynomials, rational function, composite algebraic functions, trigonometric functions, natural logarithmic and exponential functions. B. Limits of Functions 1. Definition, 2. Properties of Limits, 3. One Sided limits C. Continuity 1. Definition, 2. Theorems of Continuity, 3. Types of Discontinuity D. Derivatives 1. Slope of tangent lines, instantaneous rates of change and instantaneous velocity. 2. Definition of derivative at a point. 3. Computation of derivative using definition and rules for differentiating sums, differences, products, quotients and compositions of functions, including polynomials, rational functions, composite algebraic functions, and trigonometric functions, natural logarithmic and exponential functions. 4. Relationship between continuity and differentiability 5. Higher order derivatives, 6. Implicit Differentiation, 7. Mean Value Theorem E. Differentials 1. Definition, 2. Linear approximations F. Applications of Differentiation 1. Related rate problems, 2. Increasing and decreasing functions, 3. Velocity and acceleration 4. Extrema: first and second derivative tests, 5. Maximum/minimum problems 6. Concavity and points of inflection, 7. Asymptotes, 8. Curve sketching G. Anti-differentiation 1. Definition 2. Find anti-derivatives of polynomials, some trigonometric functions, and certain exponential functions 3. Substitution H. Riemann Integral 1. Definition, 2. Properties, 3. Mean Value Theorem for Integrals 4. Fundamental Theorem of Calculus I. Applications of Integrals 1. Volume, 2. Arclength, 3. Work, 4. Centroids of plane areas J. Application of Integrals 1. Area, 2. Numerical Integration, a. Trapezoidal Method, b. Simpson's Rule

5 Major Topics To Be Included 2 nd semester MTH 174 A. Transcendental Functions (inverse trigonometric, hyperbolic, and inverse hyperbolic) 1. Definition, 2. Properties, 3. Differentiation and integration B. Techniques of Integration 1. Substitution, 2. Integration by parts, 3. Trigonometric substitution 4. Quadratic irrationalities, 5. Partial fractions, 6. Change of limits C. Conics 1. Definition, 2. Rotation and translation transformations 3. Forms and graphs of second degree equations in x and y D. Polar Coordinates 1. Polar coordinate systems, 2. Transformation from polar to Cartesian coordinates and vice versa. 3. Polar functions, 4. Graphing, 5. Intersection of curves in polar coordinates 6. Plane areas in polar coordinate E. Parametric Equations and Vectors 1. Transformations between parametric and Cartesian coordinates, 2. Parametric functions 3. Differentiation and integration of parametric functions, 4. Length of an arc, 5. Vectors in 2 dimensions, 6. Dot product F. Indeterminate Forms 1. Definition, 2. L'Hopital's Rule (for 0/0 and / ) 3. Other indeterminate forms (0, /, 0 o, 0, 1 ) GH. Improper Integrals 1. Infinite limits of integration, 2. Comparison test for convergence 3. Infinite integrands H. Infinite Series 1. Definition of sequence and limit of a sequence 2. Definition of infinite series 3. Convergence tests for positive series 4. Alternating series (conditional and absolute convergence) 5. Power series (definition, radius of convergence, convergence tests, Maclaurin and Taylor series) 6. Taylor's Theorem and forms of the remainder

AP Calculus AB. Nevada Academic Standards that are assessable at the local level only.

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